an introduction to water activity and isotherms in food and food supplements

1. Water Activity 101

2. Water molecules
• Water molecules exhibit three types of molecular motions:
• Vibrational - intramolecular motion (i.e., motion within the molecule) that changes
the shape of the molecule
• Rotational - in-place spinning of a whole molecule and involves a change
in orientation of the molecule in three-dimensional space
• Translational - change in location of a whole molecule in three-dimensional space.
Levitt(2001)6 distinguishes two types of translational motion:
• (1) diffusion, in which the motion of the molecules is random and uncoordinated,
• (2) flow, in which the motion of the molecules is directional and concerted, usually due to a
driving force.
The types and speeds of molecular motion that can occur in water alone and
water in foods are dependent on the phase of the water (temperature and
external pressure) and, in a food system, on composition and system
kinetics (i.e., changes over time) as well.
https://helmholtz-
berlin.de/media/media/forschung/qm/theor
y-electron-dynamics/watervibrations.gif

3. Water activity : definition
• Energy is a driving force for process to happen
More Energy  More process
High Energy state (unstable)  Low Energy state (more stable)

4. Water activity : holistic definition
• Water activity (aw) is the measure of the energy status of the water in
a system
• High activity = more energy = water can do more in processes
(microbiological growth, moisture migration, chemical and physical reactions)
• Differences in Aw will dictate how moisture will move
Higher aw  Lower aw

5. Water activity : technical definition
• From technical definition, it’s the chemical potential of the water in a
system
𝜇 = 𝜇0 + 𝑅𝑇𝑙𝑛
𝑓
𝑓0
Chemical
potential
Chemical potential pure water
Gas constant x Temperature
fugacity

6. Fugacity : definition
• Fugacity is the escaping tendency of a material
• Can be measured by (water) vapor pressure above sample at fixed temperature
𝑓
𝑓0
=
𝑝
𝑝0
=
𝑣𝑎𝑝𝑜𝑟 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑜𝑓 𝑠𝑎𝑚𝑝𝑙𝑒 𝑎𝑡 𝑋 °𝐶
𝑣𝑎𝑝𝑜𝑟 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑜𝑓 𝑝𝑢𝑟𝑒 𝑤𝑎𝑡𝑒𝑟 𝑎𝑡 𝑋 °𝐶
Aw is down to the ratio between 2 pressures, therefore it is unitless and measured
on a scale of 0 (no energy) to 1 (the same energy as pure water).

7. Water activity and Moisture content
• Those 2 should not be confused as a product may contain a limited
amount of water with high fugacity or a high amount of water with
low fugacity
• Water activity should NOT be summarized as free water and bound
water

8. Water activity and Moisture content
18 % H20 5 % H20
Aw = 0.6 Aw = 0.6
Nothing will happen if you dip the cookie in the honey

9. Water activity and Moisture content
Water Activity Moisture Content
Energy Amount
Qualitative Quantitative
Driving force (thermodynamics) Not a driving force
Known standards (salt solutions) Empirical measurement with no standard
Unitless Must define wet basis or dry basis (LOD)

10. Water activity and Moisture content
Water Activity Moisture Content
Control microbial growth, moisture
migration
Adjust texture at a given water activity
Avoid caking and clumping Determine ingredient concentrations
Control chemical reaction rates Determine nutritional content
Model dry ingredient mixing Labeling requirements
Conduct shelflife

11. Water activity and Moisture content
900 g sand + 100 g H20
Aw = 0.999
10 % H20

12. Water activity and Moisture content
850 g H20 + 150 g NaCL
Aw = 0.892
85 % H20

13. Water activity and Moisture content
500 g H20 + 500 g Sucrose
Aw = 0.936
50 % H20

14. Water activity inside a BLEND
25%
25%
50%
DM = 90%
Aw = 0.125
REGULAR MACROSCOPIC VISION
Total water content = sum of individuals
Aw = ?

15. Water activity inside a BLEND
25%
25%
50%
DM = 90%
Aw = 0.125
Aw VISION
Equilibration of Aw in
function of mass ratio and
individual behaviors.
Water migrate from one
component to another
to follow Aw equilibration
Green Blue Orange
DM 85
Aw 0.25
DM 95
Aw 0.05
DM 95
Aw 0.15
Green Blue Orange
DM = X
Aw 0.125
DM = Y
Aw 0.125
DM = Z
Aw 0.125

16. Measuring water activity
Measuring vapor partial pressure on top
of the sample product can be closely
assimilated to measuring the relative
moisture of air on top of this product in
fixed conditions of temperature and
equilibrium

17. Water activity drive biological reactions
…Including the growth of micro-organism

18. Water activity and micro-organism
The control of water activity has been
mainly used for the control of food
spoilage by inhibiting the growth of
contamination flora.
Formulation strategy : decreasing water
activity
But there is more than that….
Microorganism Minimum Water Activity
Clostridium botulinum E 0.97
Pseudomonas fluorescens 0.97
Escherichia coli 0.95
Clostridium perfringens 0.95
Clostridium botulinum A, B 0.94
Salmonella spp. 0.95
Vibrio parahaemolyticus 0.94
Bacillus cereus 0.93
Listeria monocytogenes 0.92
Bacillus subtilis 0.91
Staphylococcus aureus
(anaerobic)
0.90
Staphylococcus aureus (aerobic) 0.86

19. Water activity and
micro-organism
Formulation strategy : it’s a must to know the critical level of water activity
…under various conditions.

20. Measuring sorption isotherm
By reversing the processes of water
activity measurement, we can adjust
the %RH on top of a sample and force
the water activity to adjust to the
chosen value. The resulting moisture
content will vary according to the
capacity of the material to bind water or
not

21. Brunauer, Emmett and Teller (BET)
Theory for multilayer adsorption
This theory assumes a random distribution
of sites at the surface of the material, that
are empty or that are covered with by one
monolayer, two layers and so on, of water
molecules
The water molecules of the first layers are
considered to be of low fugacity while the
ones of the external layers are of high
fugacity.
S. Brunauer, P.H. Emmett, and E. Teller, “Adsorption of Gases in
Multimolecular Layers,” J. Amer. Chem. Soc. 60, 309–319 (1938).

22. Building a sorption isotherm by applying
successive relative moisture levels at fixed temperature
Each of our product will have a
critical water activity for which :
- biological process starts
- catalytical degradation is
significant
etc…

23. Caractéristiques physiques déduites des isothermes
• Teneur en eau de transition (m0)
• Application d'une méthode
d'estimation de paramètres à
partir d'une courbe expérimentale
modélisée avec les formules BET
ou GAB
• Surface de la monocouche (Sm)
• Surface de la monocouche en
supposant que celle-ci est
recouverte de molécules alignées
• Epaisseur de la couche d'eau
adsorbée
• A la transition entre zones 2 et 3,
toute l'eau adsorbée recouvre
uniformément la surface du
produit

24. Building a sorption isotherm
Historical method : the jars
1. Incubator at fixed temperature
2. Desiccator with multiple
samples of the product
3. Plate
4. Saturated solution of salt to
control RH
x 10 for 10 points resolution isotherm curve
x 20 for 20 points resolution isotherm curve….
+ an extensive collection of saturation salts + 6 to 18 weeks

25. Building a sorption isotherm for POWDER sample
Modern method : the DVS… invented in 1993 !

26. Building a sorption isotherm for POWDER sample
Modern method : the DVS
• Micro-balance (µg) with very low drift
• High precision temperature and RH control
• Computer controlled KINETIC measure
High resolution sorption curves on smaller samples

27. Modeling a sorption isotherm
Raw data -> isotherm -> model equation
-0.14055 0.20062 0.02245
0.00648 0.00692 0.00152
0.99485 0.00172 #N/A
x0= 8.936390913
y0= -6.260700515
c2= 0.652885597
c1= 15.68752958
m0= 4.348980177
Regression Analysis Parameters
GAB MODEL 25 °C
m0 4.3490
Aw for m0 / solution 1 0.309
Aw for m0 / solution 2 -0.517
c1 15.6875
c2 0.6529
Average Rel Err 1.58%
Max Rel Err 3.26%
Max Abs Err 0.313
R² 0.9949
Rel Err > 3% 9%
𝑚
𝑚𝑜
=
𝑐1𝑐2𝑎𝑤
1 − 𝑐2𝑎𝑤 (1 − 𝑐2𝑎𝑤 + 𝑐1𝑐2𝑎𝑤
2 )
𝐴0 =
1
𝑚𝑜𝑐1𝑐2
𝐵0 =
1
𝑚𝑜
1 −
2
𝑐1
𝐶0 =
𝑐2
𝑚𝑜
1
𝑐1
− 1
𝑎𝑤
𝑚
= 𝐴0 + 𝐵0𝑎𝑤 + 𝐶0𝑎𝑤
2

28. Isotherm : Various types exist
Impacted by water interaction and micro-structure

29. Isotherm : manipulation of formula to impact the curve
At fixed composition, a substance
cannot escape its isotherm curve.
Choosing wisely quality and
quantities of the ingredients
combined with our
probiotics/molecule, will allow to
manipulate the curve.

30. Isotherm :
manipulation of formula to impact the curve

31. The over-drying strategy

32. Isotherm : manipulation of formula to impact the curve
The over-drying strategy / starting situation
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
mcal
Critical Aw
Regular Actisaf
Regular shelf life : 24 months
2 point H20  0.2 point Aw

33. Isotherm : manipulation of formula to impact the curve
The over-drying strategy / over-dried variant
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
mcal
Overdried Actisaf
Critical Aw
Extended shelf life : 36 months
3 point H20  0.25 point Aw

34. The blending strategy

35. Isotherm : manipulation of formula to impact the curve
The composition/blending strategy / starting situation
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
Probiotic
Protective Excipient
Critical Aw
0.5 for 3% H20
Regular LRGG

36. Isotherm : manipulation of formula to impact the curve
The blending strategy / blending the 2 components
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
Probiotic
Protective Excipient
Critical Aw
0.5 for 3% H20
Blend
Aw
0.2 for 3% H20

37. Isotherm : manipulation of formula to impact the curve
The blending strategy / every H20 increase impacts less Aw
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
Probiotic
Protective Excipient
Critical Aw
0.5 for 3% H20
Aw
0.1 for 2 % H20
Extended shelf life : can tolerate up to 5% H20
before reaching detrimental Aw for the probiotic

38. Isotherm : manipulation of formula to impact the curve
The blending strategy / Improved water update tolerance
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
Probiotic
Protective Excipient
Initial tolerance:
2 points H20 uptake
Improved tolerance:
3 points H20 uptake

39. Isotherm & packaging topics

40. Isotherm & packaging topics
• Film permeability can be measured with the support of a DVS
machine by using a Payne cell

41. Film permeability
• Film permeability procedure : The temperature and %RH are fixed. The sample of
film to be tested is allowing a constant flux of water vapor to be absorbed by the
drying agent.
• Knowing the surface of the film specimen tested, you can deduct from the flux a
Moisture Vapor Transmission Rate (MVTR)
X.XX g Water Vapor/ m² / hour at YY°C and ZZ %RH

42. Film permeability and shelf-life prediction
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
Critical Aw
Regular Aw
4 points H20 to
reach critical Aw
Storage 25°C – 60% RH
0.3 points Aw to
reach critical Aw
Known parameters / Example
Product mass : 25 kg
Surface of 1 bag = 0.5 m2
MVTR of the film = 0.15 g H20 / m2 / hour at 25°C and 60 %RH

43. Film permeability and shelf-life prediction
Surface of 1 bag =0.5 m2 + MVTR of the film = 0.15 g H20/m2/hour at 25°C and 60 %RH
 g of H20 for 1 bag in 1 day at 25°C and 60 %RH
 g H20 / g product in 1 day at 25°C and 60 %RH
 Increased moisture content that leads to increased Aw (via isotherm curve)
From this, you can estimate the time that will be needed to reach the critical Aw,
assuming the Fickian diffusion will remain constant along the process.

44. Water Activity 101
D.Sturm

45. Annexes : isotherms models

46. Model : BET (Brunauer-Emmet-Teller)
• The BET model is given by the following equation.
• In this equation n is the amount adsorbed at the partial pressure p, nm is the
monolayer capacity, C is the sorption constant and po the saturation pressure.
• A plot of p/[n*(po- p)] versus p/po usually gives a straight line from which nm can
be calculated.
• A good indicator for the adsorption mechanism is the isotherm shape. To apply
the BET equation there is typically a type II or IV adsorption expected.
• It should be also noted that the BET equation is only valid in a limited partial
pressure range. This range depends on the adsorptive but is typically between
0.05 and 0.4 p/p.

47. Model : GAB (Guggenheim-Anderson-DeBoer)
• The GAB model is given by the following equation.
• There have been many attempts in the past to extend the BET equation and to
make it applicable at higher partial pressures.
• One of the most successful approaches is the GAB equation , where an additional
constant has been added. Although several authors have tried to put some
physical meaning into this equation. The interpretation should be handled with
care. For this reason the GAB equation should rather be considered as semi-
empirical.

48. Model : Iglesias & Chirife
• The Iglesias & Chirife model is given by the following equation.
n0.5 is the water uptake at p/po = 0.5 and a and b are constants.
• The equation of Iglesias & Chirife [14] was developed to take dissolution effects
into account occurring at high relative humidities.
• This equation, like many other empirical formulae, do not reflect equilibrium
values and have no thermodynamic meaning. However, the equation of Iglesias &
Chirife was found to fit the water sorption behavior of many sugar-based
composites extremely well

49. Model : Smith
• The Smith model is given by the following equation.
a and b are again empirical constants.
• Smith found an equation to describe the enhanced water uptake of
macromolecular organic materials at high relative humilities
(typically 0.5 - 0.95 p/po).

50. Model : Halsey / Frenkel-Halsey-Hill
• The Halsey model is given by the following equation.
a and b are constants.
• b is related to distance of the adsorbed molecule from the surface. A high value
for b is associated with a strong interaction between surface and adsorbate
(polar) while a small value for b indicates weaker, long-range van der Waals
forces.
• The FHH equation is sometimes plotted in its linear form (log po/p vs log n).

51. Model : Henderson
• The Henderson model is given by the following equation.
• where a and b are constants. It was concluded from experimental observations
that this equation is a generalization of several localized isotherms, describing
different adsorption sites. Although a split into separate parameters for each site
would make the equation theoretically more meaningful it would loose its utility
for practical applications.

52. Model : Oswin
• The Oswin model is given by the following equation.
with a and b as constant.
• It is typically used to describe all types of water interactions with macromolecular
solids at lower partial pressures.
• The Oswin equation is a mathematical series expansion for sigmoid shaped
curves